Answer
$m=1.6$ kg
Work Step by Step
As $T_1=2\pi\sqrt\frac{m}{K}$..................... eq(1)
$T_2=2\pi\sqrt\frac{m+\Delta m}{K}$......................eq(2)
Therefore, $\frac{T_2}{T_1}$ can be written as:
$\frac{T_2}{T_1}=\sqrt\frac{m+\Delta m}{m}$
This simplifies to:
$m=\sqrt\frac{\Delta m}{(\frac{T_2}{T_1})^2-1}$
We plug in the known values to obtain:
$m=\sqrt\frac{2}{(\frac{3}{2})^2-1}=1.6$ kg
